A377764 Decimal expansion of (Pi/8)*exp(4*G/Pi), where G is the Catalan constant (A006752).

1, 2, 6, 0, 5, 2, 9, 6, 1, 2, 8, 2, 9, 3, 8, 6, 4, 1, 0, 5, 5, 4, 5, 3, 6, 3, 3, 0, 1, 3, 5, 4, 0, 9, 8, 4, 2, 2, 0, 2, 6, 6, 9, 2, 3, 9, 3, 5, 1, 5, 8, 8, 7, 2, 2, 6, 1, 0, 7, 7, 6, 8, 3, 3, 7, 3, 4, 3, 3, 9, 2, 6, 0, 5, 9, 0, 0, 9, 3, 5, 1, 1, 8, 8, 6, 7, 0, 5, 0, 7

Offset: 1

Author

Paolo Xausa, Nov 06 2024

Keywords

• nonn
• cons
• easy

Examples

			1.26052961282938641055453633013540984220266923935...
		

Links

• Michael Penn, A nice product from Ramanujan -- featuring 3 important constants!, YouTube video, 2023.

Crossrefs

Cf. A000796, A001113, A005408, A006752, A016754, A019675, A229728.

Programs

Mathematica

First[RealDigits[Pi/8*Exp[4*Catalan/Pi], 10, 100]]

Formula

Equals A019675*A229728.

Equals Product_{k >= 1} (1 - 1/(2*k+1)^2)^((-1)^k*(2*k+1)) (from Ramanujan).

Equals Product_{k >= 1} (1 - 1/A016754(k))^((-1)^k*A005408(k)).